High-efficiency multi-slot waveguide nano-opto-electromechanical phase modulator

ABSTRACT

A nano-opto-electro-mechanical System (NOEMS) phase shifter is described. The NOEMS may include a multi-slot waveguide structure suspended in air. The multi-slot waveguide structure may include three or more waveguides separated from each other by slots. The width of the slots may be sufficiently small to support slot modes, where a substantial portion of the mode energy is within the slots. For example, the slots may have widths less than 200 nm or less than 100 nm. The multi-slot waveguide structure may be disposed in a trench formed though the upper cladding of a substrate. An undercut may be formed under the multi-slot waveguide structure to enable free motion of the structure. NOEMS phase modulators of the types described herein may be used in connection with photonic processing systems, telecom/datacom systems, analog systems, etc.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Continuation claiming the benefit under 35 U.S.C. § 120 of U.S. patent application Ser. No. 16/411,476, entitled “HIGH-EFFICIENCY MULTI-SLOT WAVEGUIDE NANO-OPTO-ELECTROMECHANICAL PHASE MODULATOR,” filed on May 14, 2019, which is hereby incorporated herein by reference in its entirety.

U.S. patent application Ser. No. 16/411,476 claims the benefit under 35 U.S.C. § 119(e) to U.S. Provisional Application Ser. No. 62/792,720, entitled “HIGH-EFFICIENCY DOUBLE-SLOT WAVEGUIDE NANO-OPTOELECTROMECHANICAL PHASE MODULATOR,” filed on Jan. 15, 2019, which is hereby incorporated herein by reference in its entirety.

BACKGROUND

Phase modulators are optical devices designed to vary the phase of optical signals. In phase modulators, phase changes can be achieved by varying the refractive index of a material. Examples of mechanism for achieving refractive index variations include the free-carrier plasma dispersion and the thermo-optic effect. The free-carrier plasma dispersion effect is related to the density of free carriers in a semiconductor, which causes changes both in the real and imaginary parts of the refractive index. Hence, phase modulation can be achieved by carrier injection or depletion. The thermo-optic effect is related to changes in the refractive index of a material responsive to temperature changes. Typical thermo-optic phase modulators include doped semiconductor regions, in which a temperature rise results from the passage of electric charges.

SUMMARY OF THE DISCLOSURE

Some embodiments relate to a photonic apparatus comprising a substrate; an input optical waveguide formed on the substrate; and a suspended multi-slot optical structure optically coupled to the input optical waveguide.

In some embodiments, the suspended multi-slot optical structure comprises first, second and third optical waveguides arranged to form a first slot between the first optical waveguide and the second optical waveguide and a second slot between the second optical waveguide and the third optical waveguide.

In some embodiments, the first, second and third optical waveguides are co-planar.

In some embodiments, the first slot is sized to support more optical energy than the third optical waveguide.

In some embodiments, the first slot has a width that is equal to or less than 200 nm.

In some embodiments, the first slot has a width that is equal to or less than 100 nm.

In some embodiments, the second optical waveguide is contiguous with the input waveguide.

In some embodiments, the second optical waveguide is tapered such that the width of the second waveguide is equal to a width of the input waveguide at a distal end of the suspended multi-slot optical structure and the width of the second waveguide is less than a width of the input waveguide at a center of the suspended multi-slot optical structure.

In some embodiments, the suspended multi-slot optical structure is surrounded by air.

In some embodiments, the suspended multi-slot optical structure is free to oscillate in the air relative to the substrate.

In some embodiments, the suspended multi-slot optical structure is free to oscillate in a direction perpendicular to a propagation axis of the suspended multi-slot optical structure.

In some embodiments, the photonic apparatus further comprises a lower cladding formed on the substrate and an undercut formed through a portion of the lower cladding between the substrate and the suspended multi-slot optical structure.

In some embodiments, the lower cladding is not in contact with the suspended multi-slot optical structure.

In some embodiments, the photonic apparatus further comprises an upper cladding formed on the lower cladding and a trench formed through a portion of the upper cladding, wherein the suspended multi-slot optical structure is disposed in the trench.

In some embodiments, at least a portion of the input optical waveguide rests on the lower cladding.

In some embodiments, the suspended multi-slot optical structure is made of a material having a doping concentration less than 10¹⁴ cm⁻³.

In some embodiments, the suspended multi-slot optical structure is made of an undoped material.

Some embodiments relate to an optical phase shifter comprising a substrate; an input optical waveguide formed on the substrate; an output optical waveguide formed on the substrate; and a multi-slot optical structure optically coupling the input optical waveguide to the output optical waveguide and forming first and second slots.

In some embodiments, the multi-slot optical structure comprises first, second and third optical waveguides, the first slot being formed between the first and second optical waveguides and the second slot being formed between the second and third optical waveguides.

In some embodiments, the mechanical structure is attached to the first and third optical waveguides.

In some embodiments, motion of the mechanical structure causes a variation in a width of the first slot and/or a variation in a width of the second slot.

In some embodiments, the multi-slot optical structure has a length that is less than or equal to 50 μm.

In some embodiments, the multi-slot optical structure has a length that is less than or equal to 30 μm.

In some embodiments, the multi-slot optical structure is suspended.

In some embodiments, the optical phase shifter further comprises a lower cladding formed on the substrate and an undercut formed through a portion of the lower cladding between the substrate and the multi-slot optical structure.

In some embodiments, the lower cladding is not in contact with the multi-slot optical structure.

In some embodiments, the optical phase shifter further comprises an upper cladding formed on the lower cladding and a trench formed though a portion of the upper cladding, wherein the multi-slot optical structure is disposed in the trench.

In some embodiments, the optical phase shifter further comprises a mechanical structure connecting the multi-slot optical structure to a mechanical driver.

Some embodiments relate to a method for shifting a phase of an optical signal, the method comprising providing the optical signal to a multi-slot optical structure formed on a substrate and having first and second slots; exciting a multi-slot optical mode defined in the multi-slot optical structure; and varying a width of the first slot and/or a width of the second slot over time.

In some embodiments, at least 50% of an energy of the multi-slot mode is within the first and second slots.

In some embodiments, varying a width of the first slot and/or a width of the second slot over time comprises applying a mechanical force to the multi-slot optical structure via a mechanical structure.

In some embodiments, the multi-slot optical structure comprises first, second and third optical waveguides, wherein the first slot is formed between the first and second optical waveguides and the second slot is formed between the second and third optical waveguides, and wherein applying a mechanical force to the multi-slot optical structure comprises applying a mechanical force to the first optical waveguide and the third optical waveguide.

Some embodiments relate to a method for fabricating a photonic apparatus, the method comprising obtaining a chip having a substrate, a lower cladding layer formed on the substrate, a semiconductor layer formed on the lower cladding layer and an upper cladding layer formed on the semiconductor layer; patterning the semiconductor layer to form a multi-slot optical structure having first and second slots; forming a trench in the upper cladding layer to expose the multi-slot optical structure to air; and forming an undercut in the lower cladding layer to suspend at least a portion of the multi-slot optical structure in air.

In some embodiments, patterning the semiconductor layer to form the multi-slot optical structure comprises patterning the semiconductor layer to form first, second and third optical waveguides, the first slot being disposed between the first and second optical waveguides and the second slot being disposed between the second and third optical waveguides.

In some embodiments, forming the trench in the upper cladding layer comprises performing a reactive ion etch through the upper cladding layer.

In some embodiments, forming the undercut in the lower cladding layer comprises performing an isotropic etch through the lower cladding layer.

Some embodiments relate to a nano-opto-electro-mechanical System (NOEMS) phase shifter comprising: a plurality of non-conductive waveguides suspended in a trench.

In some embodiments, each of the plurality of non-conductive waveguides has a resistivity greater than 1300 Ωcm.

In some embodiments, adjacent waveguides of the plurality of non-conductive waveguides are separated from each other by less than 200 nm.

In some embodiments, the NOEMS phase shifter further comprises a mechanical driver configured to cause oscillation of at least some of the plurality of non-conductive waveguides.

BRIEF DESCRIPTION OF THE DRAWINGS

Various aspects and embodiments of the application will be described with reference to the following figures. It should be appreciated that the figures are not necessarily drawn to scale. Items appearing in multiple figures are indicated by the same reference number in all the figures in which they appear.

FIG. 1A is a top view illustrating schematically a Nano-Opto-Electromechanical Systems (NOEMS) phase modulator, in accordance with some non-limiting embodiments.

FIG. 1B is a top view illustrating schematically a suspended multi-slot optical structure of the NOEMS phase modulator of FIG. 1A, in accordance with some non-limiting embodiments.

FIG. 1C is a plot illustrating an example of an optical mode arising in the suspended multi-slot optical structure of FIG. 1B, in accordance with some non-limiting embodiments.

FIG. 1D is a top view illustrating schematically a mechanical structure of the NOEMS phase modulator of FIG. 1A, in accordance with some non-limiting embodiments.

FIG. 1E is a top view illustrating schematically a transition region of the NOEMS phase modulator of FIG. 1A, in accordance with some non-limiting embodiments.

FIG. 2 is a cross-sectional view of the NOEMS phase modulator of FIG. 1A, taken in a yz-plane, and illustrating a suspended waveguide, in accordance with some non-limiting embodiments.

FIG. 3 is a cross-sectional view of the NOEMS phase modulator of FIG. 1A, taken in a xy-plane, and illustrating a portion of a suspended multi-slot optical structure, in accordance with some non-limiting embodiments.

FIGS. 4A-4C are cross-sectional views illustrating how a suspended multi-slot optical structure can be mechanically driven to vary the widths of the slots between the waveguides, in accordance with some non-limiting embodiments.

FIG. 5 is a plot illustrating how the effective index of a suspended multi-slot optical structure may vary as a function of the width of a slot, in accordance with some non-limiting embodiments.

FIG. 6 is a flowchart illustrating an example of a method for fabricating a NOEMS phase modulator, in accordance with some non-limiting embodiments.

DETAILED DESCRIPTION

The inventors have recognized and appreciated that certain optical phase modulators suffer from high dynamic loss and low modulation speed, which significantly limit the range of applications in which these phase modulators can be deployed. More specifically, some phase modulators involve significant trade-offs between modulation speed and dynamic loss, such that an increase in modulation speed results in an increase in dynamic loss. As used herein, the phrase “dynamic loss” refers to optical power loss experienced by an optical signal that depends on the degree to which its phase is modulated. Ideal phase modulators are such that power loss is independent of the phase modulation. Real-world phase modulators, however, experience a certain power loss when no modulation occurs, and experience a different power loss when modulation occurs. For example, the power loss experienced at no phase modulation may be L₁, the power loss experienced at a π/2-phase modulation may be L₂, and the power loss experienced at a π-phase modulation may be L₃, with L₁, L₂ and L₃ being different from each other. This behavior is undesirable because, in addition to phase modulation, the signal further experiences amplitude modulation.

Some such phase modulators, in addition, require several hundreds of microns in length to provide sufficiently large phase shifts. Unfortunately, being so long, such phase modulators are not suitable for use in applications requiring integration of several phase shifters on a single chip. The phase modulators alone may take up most of the space available on the chip, thus limiting the number of devices that can be co-integrated on the same chip.

Recognizing the aforementioned limitations of certain phase modulators, the inventors have developed small footprint-optical phase modulators capable of providing high modulation speeds (e.g., in excess of 100 MHz or 1 GHz) while limiting dynamic loss. In some embodiments, a phase modulator may occupy an area as small as 300 μm². Thus, as an example, a reticle having an area of 1 cm² can accommodate as many as 15,000 phase modulators while saving an additional 50 mm² for other devices.

Some embodiments relate to Nano-Opto-Electromechanical Systems (NOEMS) phase modulators having multiple suspended optical waveguides positioned adjacent to one another and forming a plurality of slots therebetween. The dimensions of the slots are sufficiently small to form slot waveguides, whereby a substantial portion (e.g., a majority) of the mode energy is confined in the slots themselves. These modes are referred to herein as slot modes. Having a substantial portion of the mode energy in the slots enables modulation of the effective index of the mode, and a result, of the phase of an optical signal embodying the mode, by causing variations in the dimensions of the slots. In some embodiments, phase modulation can be achieved by applying mechanical forces that cause variations in the dimensions of the slots.

The inventors have recognized and appreciated that the modulation speed achievable with the NOEMS phase modulators described herein can be increased, without significant increases in dynamic loss, by decoupling the mechanical drivers from the region where optical modulation takes place. In phase modulators in which the mechanical drivers are decoupled from the optical modulation region, electric driving signals are applied on the mechanical drivers, rather than being applied on the optical modulation region itself. This arrangement removes the need to make the optical modulation region electrically conductive, thus enabling a reduction in the doping of this region. The low doping results in a reduction of free carriers which may otherwise lead to optical absorption, thus lowering dynamic loss.

Furthermore, decoupling the mechanical drivers from the optical modulation region enables a greater modulation per unit length, and as a result a shorter modulation region. Shorter modulation regions, in turn, enable, greater modulation speed.

The inventors have further recognized and appreciated that including multiple slots in the modulation region can enable a further reduction in the length of the phase modulator (thereby decreasing its size). Having more than one slot, in fact, enables a substantial reduction in the length of the transition region through which light is coupled to the modulation region. The result is a substantially more compact form factor. Thus, NOEMS phase modulators of the types described herein can have shorter modulation regions and/or shorter transition regions. Phase modulators of the types described herein can have lengths as low as 20 μm or 30 μm, in some embodiments.

As will be described in detail further below, some embodiments relate to phase modulators in which a trench is formed in the chip, and is arranged so that the modulating waveguides are suspended in air and are free move in space.

The inventors have recognized a potential drawback associated with the use of trenches that results from the formation of cladding/air interfaces. When a propagating optical signal enters (or exits) a trench, it encounters a cladding/air interface (or an air/cladding interface). Unfortunately, the presence of the interface can give rise to optical reflections, which in turn can increase insertion losses. The inventors have appreciated that the negative effect of such interfaces can be mitigated by reducing the physical extension of the optical mode in the region where it passes through the interface. This can be achieved in various ways. For example, in some embodiments, the extension of the optical mode may be reduced by tightly confining the mode within a rib waveguide. A rib waveguide may be sized so that only a small fraction of the mode energy (e.g., less than 20%, less than 10%, or less than 5%) is outside the edges of the waveguide.

NOEMS phase modulators of the types described herein may be used in a variety of applications, including for example in telecom and datacom (including local area networks, metropolitan area networks, wide area networks, data center networks, satellite networks, etc.), analog applications such as radio-over-fiber, all-optical switching, coherent Lidar, phased arrays, coherent imaging, machine learning and other types of artificial intelligence applications. Additionally, the NOEMS modulators may be used as part of amplitude modulators, for example if combined with a Mach Zehnder modulator. For example, a Mach Zehnder modulator may be provided in which a NOEMS phase modulator is positioned in one or more of the arms of the Mach Zehnder modulator. Several modulation schemes may be enabled using NOEMS phase modulators, including for example amplitude shift keying (ASK), quadrature amplitude modulation (QAM), phase shift keying (BPSK), quadrature phase shift keying (QPSK) and higher order QPSK, offset quadrature phase-shift keying (OQPSK), Dual-polarization quadrature phase shift keying (DPQPSK), amplitude phase shift keying (APSK), etc. Additionally, NOEMS phase modulators may be used as phase correctors in applications in which the phase of an optical signal tends to drift unpredictably. In some embodiments, NOEMS phase modulators of the types described herein may be used as part of a photonic processing system.

FIG. 1A is a top view illustrating schematically a Nano-Opto-Electromechanical Systems (NOEMS) phase modulator, in accordance with some non-limiting embodiments. NOEMS phase modulator 100 includes input waveguide 102, output waveguide 104, input transition region 140, output transition region 150, suspended multi-slot optical structure 120, mechanical structures 130 and 132, and mechanical drivers 160 and 162. NOEMS phase modulator 100 may be fabricated using silicon photonic techniques. For example, NOEMS phase modulator 100 may be fabricated on a silicon substrate, such as a bulk silicon substrate or a silicon-on-insulator (SOI) substrate. In some embodiments, NOEMS phase modulator 100 may further include electronic circuitry configured to control the operations of mechanical drivers 160 and 162. The electronic circuitry may be fabricated on the same substrate hosting the components of FIG. 1A, or on a separate substrate. When disposed on a separate substrate, the substrates may be bonded to one another in a any suitable way, including 3D-bonding, flip-chip bonding, wire bonding etc.

At least part of NOEMS phase modulator 100 is formed in a trench 106. As will be described in detail further below, trenches of the types described herein may be formed by etching a portion of the cladding. In the example of FIG. 1A, trench 106 has a rectangular shape, though trenches of any other suitable shape may be used. In this example, trench 106 has four sidewalls. Sidewalls 112 and 114 are spaced from one another along the z-axis (referred to herein as the propagation axis), and the other two sidewalls (not labeled in FIG. 1A) are spaced from one another along the x-axis.

In some embodiments, the separation along the z-axis between sidewalls 112 and 114 may be less than or equal to 50 μm, less than or equal to 30 μm, or less than or equal to 20 μm. Thus, the modulation region of this NOEMS phase modulator is significantly shorter than other types of phase modulators, which require several hundreds of microns for modulating the phase of an optical signal. The relatively short length is enable by one or more of the following factors. First, having multiple slots improves coupling to the optical modulation region, which in turn enables a reduction in the length of the transition region. The improved coupling may be the result of enhanced mode symmetry in the multi-slot structure. Second, decoupling the mechanical drivers from the optical modulation region enables a greater modulation per unit length, and as a result a shorter modulation region.

During operation, an optical signal may be provided to input waveguide 102. In one example, the optical signal may be a continuous wave (CW) signal. Phase modulation may take place in suspended multi-slot optical structure 120. A phase modulated optical signal may exit NOEMS phase modulator 100 from output waveguide 104. Transition region 140 may ensure loss-free or nearly loss-free optical coupling between input waveguide 102 and suspended multi-slot optical structure 120. Similarly, transition region 150 may ensure loss-free or nearly loss-free optical coupling between suspended multi-slot optical structure 120 and output waveguide 104. Transitions regions 140 and 150 may include tapered waveguides in some embodiments, as described in detail further below. As discussed above, the length of the transitions regions may be shorter relative to other implementations.

The input optical signal may have any suitable wavelength, including but not limited to a wavelength in the O-band, E-band, S-band, C-band or L-band. Alternatively, the wavelength may be in the 850 nm-band or in the visible band. It should be appreciated that NOEMS phase modulator 100 may be made of any suitable material, so long as the material is transparent or at least partially transparent at the wavelength of interest, and the refractive index of the core region is greater than the refractive index of the surrounding cladding. In some embodiments, NOEMS phase modulator 100 may be made of silicon. For example, input waveguide 102, output waveguide 104, input transition region 140, output transition region 150, suspended multi-slot optical structure 120, and mechanical structures 130 and 132 may be made of silicon. Given silicon's relatively low optical bandgap (approximately 1.12 eV), silicon may be particularly suitable for use in connection with near infrared wavelengths. In another example, NOEMS phase modulator 100 may be made of silicon nitride or diamond. Given silicon nitride's and diamond's relatively high optical bandgaps (approximately 5 eV and approximately 5.47 eV, respectively), these materials may be particularly suitable for use in connection with visible wavelengths. However, other materials are also possible, including indium phosphide, gallium arsenide, and or any suitable III-V or II-VI alloy.

In some embodiments, input waveguide 102 and output waveguide 104 may be sized to support a single mode at the wavelength of operation (though multi-mode waveguides can also be used). For example, if a NOEMS phase modulator is designed to operate at 1550 nm (though of course, not all embodiments are limited in this respect), input and output waveguides 102 and 104 may support a single mode at 1550 nm. In this way, the mode confinement within the waveguide may be enhanced, thus reducing optical losses due to scattering and reflections. Waveguides 102 and 104 may be rib waveguides (e.g., with rectangular cross sections) or may have any other suitable shape.

As described above, part of NOEMS phase modulator 100 may be formed within a trench 106, so that the waveguides in the modulation region are surrounded by air and are free to move in space. The drawback of including a trench is the formation of a cladding/air interface and an air/cladding interface along the propagation path. Thus, the input optical signal passes a cladding/air interface (in correspondence with sidewall 112) before reaching the region where modulation occurs and passes an air/cladding interface (in correspondence with sidewall 114) after the modulation region. These interfaces may introduce reflection losses. In some embodiments, reflection losses may be reduced by positioning transition region 140 inside, rather than outside, trench 106 (as shown in FIG. 1A). In this way, the mode expansion associated with the transition region takes place where the optical signal has already passed the cladding/air interface. In other words, the mode is tightly confined as it passes the cladding/air interface, but is expanded in the trench, using the transition region, for purposes of coupling to the suspended multi-slot structure 120. Similarly, transition region 150 may be formed inside trench 106, thereby spatially re-confining the mode before it reaches sidewall 114.

FIG. 1B illustrates suspended multi-slot optical structure 120 in additional detail, in accordance with some non-limiting embodiments. In the example of FIG. 1B, multi-slot optical structure 120 includes three waveguides (121, 122 and 123). Slot 124 separates waveguide 121 from waveguide 122 and slot 125 separates waveguide 122 from waveguide 123. The width of the slots (d₁ and d₂) may be less than the critical width (at the wavelength of operation) for forming slot modes, whereby a substantial portion of the mode energy (e.g., more than 40%, more than 50%, more than 60%, or more than 75%) is within the slots. For example, each of d₁ and d₂ may be equal to or less than 200 nm, equal to or less than 150 nm, or equal to or less than 100 nm. The minimum width may be set by the photolithographic resolution.

FIG. 1C is a plot illustrating an example of an optical mode supported by the waveguides 121, 122 and 123, in accordance with some non-limiting embodiments. More specifically, the plot illustrates the amplitude of a mode (e.g., the electric field E_(x), E_(y) or E_(z), or magnetic field H_(x), H_(y) or H_(z)). As illustrated, a substantial portion of the overall energy is confined within the slots, where the mode exhibits peaks of amplitude. In some embodiments, there is more optical energy in one of the slots than in any one of the individual waveguides. In some embodiments, there is more optical energy in one of the slots than in all the waveguides considered together. Outside the outer walls of the exterior waveguides, the mode energy decays (for example exponentially).

Widths d₁ and d₂ may be equal to, or different than, one another. The widths of the slots and the waveguides may be constant along the z-axis (as in FIG. 1B) or may vary. In some embodiments, the widths of waveguides 121, 122 and 123 may be less than the width of input waveguide 102. In some embodiments, when the wavelength of operation is in the C-band, the widths of waveguides 121, 122 and 123 may be between 200 nm and 400 nm, between 250 nm and 350 nm, or within any other suitable range, whether within or outside such ranges.

While the example of FIG. 1B illustrates suspended a multi-slot optical structure 120 with three waveguides and two slots, any other suitable number of waveguides and slots may be used. In other examples, a suspended multi-slot optical structure 120 may include five waveguides and four slots, seven waveguides and six slots, nine waveguides and eight slots, etc. In some embodiments, the structure includes an odd number of waveguides (and consequently, an even number of slots) so that only symmetric modes are excited, while antisymmetric modes remain unexcited. The inventors have appreciated that enhancing the symmetry of the mode enhances coupling into the slotted structure, thus enabling a substantial reduction in the length of the transition region. However, implementations with even number of waveguides are also possible.

As will be described in detail further below, phase modulation occurs by causing the exterior waveguides (121 and 123 in FIG. 1B) to move relative to the center waveguide (122 in FIG. 1B) along the x-axis. When waveguide 121 moves in the x-axis relative to waveguide 122, the width of slot 124 varies, and the shape of the mode supported by the structure varies accordingly. The result is a change in the effective index of the mode supported by the structure, and consequently, a phase modulation takes place. Motion of the exterior waveguides may be induced using mechanical structures 130 and 132.

An example of a mechanical structure 130 is illustrated in FIG. 1D, in accordance with some non-limiting embodiments. Mechanical structure 132 (see FIG. 1A) may have a similar arrangement. In the example of FIG. 1D, mechanical structure 130 includes beams 133, 134, 135 and 136. Beam 133 connects mechanical driver 160 to beam 134. Beams 135 and 136 connect beam 134 to the exterior waveguide. To limit optical losses, beams 135 and 136 may be attached to the exterior waveguide in the transition regions 140 and 150, respectively, rather than in the modulation region (as shown in FIG. 1E, which is discussed below). However, attaching beams 135 and 136 to the exterior waveguide to the modulation region is also possible. Beams with different shapes, sizes and orientations may be used in alternative or in addition to those illustrated in FIG. 1D.

Mechanical structure 130 may transfer mechanical forces generated at mechanical driver 160 to waveguide 121, thereby causing waveguide 121 to move relative to waveguide 122. Mechanical drivers 160 and 162 may be implemented in any suitable way. In one example, the mechanical drivers may include piezoelectric devices. In one example, the mechanical drivers may include conductive fingers. When a voltage is applied between adjacent fingers, the fingers may experience acceleration, thus imparting a mechanical force to the mechanical structures. In some embodiments, the mechanical drivers may be driven with an electrical signal having a pattern encoded thereon. In this way, modulation results in the pattern being imparted onto the phase of an input optical signal.

It should be appreciated that, because the waveguides of suspended multi-slot optical structure 120 are driven using external mechanical drivers, rather than being directly supplied with electrical signals as in certain conventional phase modulators, the conductivity of the waveguides can be relaxed, thus reducing free carrier absorption loss, and consequently, dynamic loss. This is different than some conventional phase modulators, where the waveguide itself is doped to act as a heater or a carrier accumulation region. In some embodiments, waveguides 121, 122 and 123 may be made of an undoped, or low-doped, semiconductor material (e.g., undoped silicon or silicon with a doping concentration less than 10¹⁴ cm⁻³). In some embodiments, the resistivity of the material forming the waveguides may be greater than 1300 Ωcm.

FIG. 1E illustrates an example of a transition region 140, in accordance with some non-limiting embodiments. In this implementation, waveguide 122 is contiguous to (e.g., is the continuation of) input waveguide 102. As shown, waveguide 122 is tapered in the transition region such that its width reduces as it approaches the suspended multi-slot optical structure 120. By contrast, waveguides 121 and 123 are tapered in the transition region such that their widths increase as they depart from suspended multi-slot optical structure 120. The tapered waveguides may allow adiabatic coupling between the mode of input waveguide 102 and the mode of suspended multi-slot optical structure 120, thereby limiting coupling losses. A similar arrangement may be used for transition region 150. Due to the enhanced symmetry of the mode supported by the multi-slot structure, transition regions 140 and 150 are significantly shorter than other implementations. In some embodiments, the transition regions may be as short as 10 μm or less, or 5 μm or less, though other values are also possible.

FIG. 2 is a cross sectional view of a NOEMS phase modulator 100 taken in a yz-plane passing through waveguide 122 (see plane 190 in FIG. 1B), in accordance with some non-limiting embodiments. Input waveguide 102 and output waveguide 104 are surrounded by a cladding made of a material (e.g., silicon oxide) with a refractive index lower than the refractive index of the core material. Lower cladding 202 is between the waveguide and the underlying substrate 201. Upper cladding 206 is formed over the waveguide.

To enable free motion of the waveguides of the suspended multi-slot optical structure 120, a trench 106 is formed through part of upper cladding 206. In some embodiments, a portion of the lower cladding 202 is removed under the suspended multi-slot optical structure 120, thus forming an undercut 204. As a result, waveguides 121, 122 and 123 are suspended in air and are free to move responsive to mechanical forces. A cladding/air interface exists at trench sidewall 112 and an air/cladding interface exists at trench sidewall 114. The sidewalls may be substantially vertical, for example if the trench is formed by reaction ion etching (RIE), or may alternatively be angled. Undercut 204 may have curved sidewalls, as illustrated in FIG. 2, if an isotropic etch is used, or may alternatively be substantially vertical. In some embodiments, trench 106 and undercut 204 may be formed as part of the same etch, while in other embodiments, they be formed using separate etches.

FIG. 3 is a cross sectional view of a NOEMS phase modulator 100 taken in a xy-plane passing through waveguides 121, 122 and 123 (see plane 191 in FIG. 1B), in accordance with some non-limiting embodiments. FIG. 3 shows that waveguides 121, 122 and 123 and beams 134, are co-planar (at least in this example), and are suspended in air above substrate 201. As further illustrated in this figure, waveguides 121, 122 and 123 do not contact lower cladding 202 at this cross section. When mechanical drivers 160 and 162 are actuated, beams 134 and waveguides 121 and 123 oscillate along the x-axis, thus varying the widths of the slots 124 and 125. An example of an oscillatory motion of waveguides 121 and 123 is illustrated, collectively, in FIGS. 4A-4C, in accordance with some non-limiting embodiments. FIG. 4A illustrates a case in which no mechanical force is applied. As a result, the widths of the slots are unperturbed. In FIG. 4B, a pair of forces is applied such that both waveguides 121 and 123 move towards waveguide 122, as illustrated by the arrows. As a result, the widths of the slots are reduced. In FIG. 4C, a pair of forces is applied such that both waveguides 121 and 123 move away from waveguide 122, also illustrated by the arrows. As a result, the widths of the slots are increased. In some embodiments, the forces may be applied in a periodic fashion, and/or following the pattern of the driving electrical signals. In some embodiments, the forces may be applied to waveguides 121 and 123 differentially, such that the same intensity is applied to both waveguides but with opposite signs.

FIG. 5 is a plot illustrating how the effective refractive index (Neff) of the mode propagating in the suspended multi-slot optical structure 120 varies as a function of width d₁ (the width of the slot between waveguides 121 and 122), in accordance with some non-limiting embodiments. A similar response may be plotted as a function of d₂. The effective index variation is caused by the fact that, as the separation between the waveguides varies under the effect of an applied mechanical force, the shape of the mode deviates relative to the one illustrated in FIG. 1C. As the width varies over time, so does the mode effective index, and consequently, the phase of the mode.

FIG. 6 is a flowchart illustrating an example of a method for fabricating a NOEMS phase modulator, in accordance with some non-limiting embodiments. It should be appreciated that the steps of the method described below may be performed in any suitable order, as fabrication processes are not limited to the specific order illustrated in FIG. 6.

Fabrication method 600 begins at step 602, in which a chip is obtained. In some embodiments, the chip may be a silicon-on-insulator chip, or a bulk silicon chip. The chip may have a substrate and any of the following layers: a lower cladding layer, a semiconductor layer and an upper cladding layer. The lower cladding layer may comprise silicon oxide in some embodiments. The semiconductor layer may comprises silicon, silicon nitride and/or doped silicon oxide in some embodiments. The upper cladding layer may comprise the same material forming the lower cladding layer, or a different material. FIG. 3. Illustrates an examples of a substrate (substrate 201) having a lower cladding layer (cladding 202), a semiconductor layer (the layer of waveguides 121, 122 and 123) and an upper cladding layer (cladding 206). It should be appreciated that any of the layers identified above may already be present on the chip when the chip arrives at the fabrication facility (where the NOEMS phase modulator is fabricated), or may be formed at the facility as part of the fabrication process.

At step 604, the semiconductor layer is patterned form a multi-slot optical structure having first and second slots (or any other number of slots greater than two). In the example of FIG. 3, waveguides 121, 122 and 123 may be formed at step 604. Patterning the semiconductor layer may involve deposition of a photoresist layer, a photolithographic exposure and etching through the semiconductor layer. In some embodiments, any one of mechanical structures 130 and 132, mechanical drivers 160 and 162, waveguides 102 and 104 and transition regions 140 and 142 (see FIG. 1A) are fabricated as part of the same photolithographic exposure, though not all embodiments are limited in this respect as one or more separate photolithographic exposures may be used. In some embodiments, at step 604, mechanical drivers 160 may be doped, for example using ion implantation. In some embodiments, the multi-slot optical structure may remain undoped.

At step 606, a trench may be formed through the upper cladding layer. An example of a trench (trench 106) is illustrated at FIG. 3. The trench may be formed, for example, using a dry etch such as a reactive ion etch. However, wet etches may alternatively or additionally be used. Formation of the trench may involve removal of a portion of the upper cladding layer in a region above the multi-slot optical structure formed at step 604. As a result, the multi-slot optical structure may be exposed, partially or entirely, to air.

At step 608, an undercut may be formed in the lower cladding layer. An example of an undercut (undercut 204) is illustrated at FIG. 3. The undercut may be formed, for example, using a wet etch, though dry etches may alternatively or additionally be used. Formation of the undercut may involve removal of a portion of the lower cladding layer in a region under the multi-slot optical structure. As a result, at least part of the multi-slot optical structure may be suspended over air.

Having thus described several aspects and embodiments of the technology of this application, it is to be appreciated that various alterations, modifications, and improvements will readily occur to those of ordinary skill in the art. Such alterations, modifications, and improvements are intended to be within the spirit and scope of the technology described in the application. It is, therefore, to be understood that the foregoing embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, inventive embodiments may be practiced otherwise than as specifically described. In addition, any combination of two or more features, systems, articles, materials, and/or methods described herein, if such features, systems, articles, materials, and/or methods are not mutually inconsistent, is included within the scope of the present disclosure.

Also, as described, some aspects may be embodied as one or more methods. The acts performed as part of the method may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts simultaneously, even though shown as sequential acts in illustrative embodiments.

All definitions, as defined and used herein, should be understood to control over dictionary definitions, definitions in documents incorporated by reference, and/or ordinary meanings of the defined terms.

The indefinite articles “a” and “an,” as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean “at least one.”

The phrase “and/or,” as used herein in the specification and in the claims, should be understood to mean “either or both” of the elements so conjoined, i.e., elements that are conjunctively present in some cases and disjunctively present in other cases.

As used herein in the specification and in the claims, the phrase “at least one,” in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase “at least one” refers, whether related or unrelated to those elements specifically identified.

The terms “approximately” and “about” may be used to mean within ±20% of a target value in some embodiments, within ±10% of a target value in some embodiments, within ±5% of a target value in some embodiments, and yet within ±2% of a target value in some embodiments. The terms “approximately” and “about” may include the target value. 

What is claimed is:
 1. A method for shifting a phase of an optical signal, the method comprising: providing the optical signal to a multi-slot optical structure formed on a substrate and having first, second and third optical waveguides arranged to form a first slot between the first optical waveguide and the second optical waveguide and a second slot between the second optical waveguide and the third optical waveguide; exciting a multi-slot optical mode defined in the multi-slot optical structure, the multi-slot optical mode has a first peak amplitude in the first optical waveguide and a second peak amplitude in the first slot, wherein the second peak amplitude is larger than the first peak amplitude; and varying a width of the first slot and/or a width of the second slot over time.
 2. The method of claim 1, wherein the first and second peak amplitudes are electric field peak amplitudes.
 3. The method of claim 1, wherein varying a width of the first slot and/or a width of the second slot over time comprises applying a mechanical force to the multi-slot optical structure via a mechanical structure.
 4. The method of claim 3 wherein applying a mechanical force to the multi-slot optical structure comprises: applying the mechanical force to the first optical waveguide and the third optical waveguide.
 5. The method of claim 1, wherein varying a width of the first slot and/or a width of the second slot over time comprises: increasing the width of the first slot and, simultaneously, increasing the width of the second slot.
 6. The method of claim 5, varying a width of the first slot and/or a width of the second slot over time further comprises: reducing the width of the first slot and, simultaneously, reducing the width of the second slot.
 7. The method of claim 1, wherein providing the optical signal to a multi-slot optical structure comprises adiabatically coupling the optical signal to the multi-slot optical structure using a tapered optical waveguide.
 8. The method of claim 1, wherein the multi-slot optical mode is a symmetric mode.
 9. A method for modulating a phase of an optical signal, the method comprising: providing the optical signal to a multi-slot optical structure formed on a substrate and having first, second and third co-planar suspended optical waveguides arranged to form a first slot between the first optical waveguide and the second optical waveguide and a second slot between the second optical waveguide and the third optical waveguide, wherein at least one of the first, second and third suspended optical waveguides has two fixed portions connected to the substrate and is suspended between the two fixed portions; exciting a multi-slot optical mode defined in the multi-slot optical structure; and varying a width of the first slot and/or a width of the second slot over time.
 10. The method of claim 9, wherein varying a width of the first slot and/or a width of the second slot over time comprises: moving the first optical waveguide relative to the second optical waveguide and/or moving the third optical waveguide relative to the second optical waveguide.
 11. The method of claim 9, wherein varying a width of the first slot and/or a width of the second slot over time comprises: moving the first optical waveguide towards the second optical waveguide and, simultaneously, moving the third optical waveguide towards the second optical waveguide.
 12. The method of claim 11, wherein varying a width of the first slot and/or a width of the second slot over time further comprises: moving the first optical waveguide away from the second optical waveguide and, simultaneously, moving the third optical waveguide away from the second optical waveguide.
 13. The method of claim 11, wherein moving the first and third optical waveguides comprises moving the first and third optical waveguides inside a trench in which the first, second and third optical waveguides are disposed, the trench being formed in the substrate.
 14. The method of claim 9, wherein providing the optical signal to a multi-slot optical structure comprises adiabatically coupling the optical signal to the multi-slot optical structure using a tapered optical waveguide.
 15. The method of claim 9, wherein varying a width of the first slot and/or a width of the second slot over time comprises applying an electrical modulating signal to a mechanical actuator connected to the multi-slot optical structure.
 16. A method for modulating a phase of an optical signal, the method comprising: adiabatically coupling the optical signal to a multi-slot optical structure formed on a substrate and having first, second and third co-planar suspended optical waveguides arranged so that the second optical waveguide is positioned between the first optical waveguide and the third optical waveguide; exciting a multi-slot optical mode defined in the multi-slot optical structure; and varying a separation between the first and second optical waveguides and/or varying a separation between the third and second optical waveguides.
 17. The method of claim 16, wherein adiabatically coupling the optical signal to a multi-slot optical structure comprises transmitting the optical signal through a tapered optical waveguide.
 18. The method of claim 16, wherein transmitting the optical signal through a tapered optical waveguide comprises exciting an optical mode configured to laterally expand as the optical signal propagates along the tapered optical waveguide.
 19. The method of claim 16, wherein varying a separation between the first and second optical waveguides and/or varying a separation between the third and second optical waveguides comprises: moving the first optical waveguide relative to the second optical waveguide and/or moving the third optical waveguide relative to the second optical waveguide.
 20. The method of claim 16, wherein varying a separation between the first and second optical waveguides and/or varying a separation between the third and second optical waveguides comprises: moving the first optical waveguide towards the second optical waveguide and, simultaneously, moving the third optical waveguide towards the second optical waveguide. 